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Q.

∫sin2xsin5xsin3xdx =

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a

13log sin3x-log sin5x+c

b

13log sin3x+15log sin5x+c

c

13log sin3x-15log sin5x+c

d

3log sin3x-5log sin5x+c

answer is C.

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Detailed Solution

∫sin2xsin5xsin3xdx =∫sin(5x-3x)sin5xsin3xdx  =∫sin5xcos3x-cos5xsin3xsin5xsin3xdx  =∫(cot3x-cot5x)dx =13logsin3x-15logsin5x+c
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∫sin2xsin5xsin3xdx =